Rigging technique for flexible cardboard packaging
To make sure that the slot is sharp and to avoid unpleasant mesh folding, you need to rework the topology and bring a new bone that overlap the slot. Now parent With Automatic Weight again, give your object a Subdivision Surface modifier (with a Subdivision of 2), and right click and Shade Smooth:


The way you wanted to mirror your animation is not the right one, you need to create bones for the left part. Apply the rotation of your armature, create a root bone, change the name of your bones to bone1.R, bone2.R, etc, symmetrize your armature:

Delete the Armature modifier of your object, parent again, for example With Automatic Weight, switch to Weight Paint mode, set your brush correctly, give some corrections so that it works the way you want:


If you want the left bones to copy what happens to the other side, give them Copy Rotation constraints:

The blend file: